Exam 7: Probability

Use the following information for questions: It seems that every year we hear about a train derailment. Discussions about the safety of train travel are initiated each time. Suppose there have been nine fatal train derailments over the past 10 years. However, each year, 5 million train trips depart (this does not include subway travel). -Which of the following is not a correct interpretation of these numbers?

When two dice are rolled, there are 36 possible outcomes. Six of these outcomes have two the same numbers (two ones, two twos, etc.). The chance of getting two of the same numbers when rolling two dice is 6/36 or 0.1667. What is the chance of getting 2 numbers that are different from one another?

Which of the following statements is true for tossing a fair coin (i.e. Probability of Heads = ½) if the first 100 tosses of the coin result in 100 heads?

Tickets for an upcoming concert are sold out but a local charity is having a raffle and the prize is a pair of tickets to the concert. One hundred people enter the raffle, so each individual who entered has 1/100 probability of winning the pair of tickets. You and a friend both entered. What is the probability that one or the other of you wins the tickets?

Imagine a test for a certain disease. Suppose the probability of a positive test result is 0.95 if someone has the disease, but the probability is only 0.08 that someone has the disease if his or her test result was positive. A patient receives a positive test, and the doctor tells him that he is very likely to have the disease. The doctor's response is

Use the following information for questions: A statistics class has 4 teaching assistants (TAs): three female assistants (Lauren, Rona, and Leila) and one male assistant (Josh). Each TA teaches one discussion section. -A student picks a discussion section. The two events W = {the TA is a woman} and J = {the TA is Josh} are

Use the following information for questions: A student is randomly selected from a large college campus. Define the eventsH = {the student has blond hair} and E = {the student has blue eyes}. -The chance that a blond haired student has blue eyes equals 75%. How do we write this probability?

A thumbtack is tossed repeatedly and observed to see if the point lands resting on the floor or sticking up in the air. The goal is to estimate the probability that a thumbtack would land with the point up. That probability is an example of

A six-sided die is made that has four Green sides and two Red sides, all equally likely to land face up when the die is tossed. The die is tossed three times. Which of these sequences (in the order shown) has the highest probability?

Assuming that a person has an equal chance of being born on any day of a 365-day year, what is the chance that two people chosen at random will have different birthdays?

Use the following information for questions: Thirty percent of the students in a high school face a disciplinary action of some kind before they graduate. Of those students, 40% go on to college. Of the 70% who do not face a disciplinary action, 60% go on to college. -What percent of the students from the high school go on to college?

Two standard 52-card decks are shuffled and two cards are picked at random - one card from each deck. The probability that two Hearts are drawn is

Use the following information for questions: For each situation, decide if the probability described is a subjective (personal) probability or a relative frequency probability. -A quarter is flipped 2000 times and results in 500 heads. The 25% (500/2000) chance of heads is a

Lauren wants to wear something warm when she leaves for class. She reaches into her coat closet without looking and grabs a hanger. Based on what she has in her coat closet, she has a 30% chance of picking a sweater, a 50% chance of picking a coat, and a 20% chance of picking a jacket. What is the probability that she will pick a sweater or a coat?

Belgium has two official languages, French and Dutch. Assume that about 60% of the people use Dutch as their primary language and 40% of the people use French as their primary language. We are about to randomly select 3 Belgians. We wish to calculate the probability that the 3 people speak the same language. Explain how you would choose random digits to simulate this scenario.

Which of the following is not necessarily true for independent events A and B?

Use the following information for questions: In the past five years, only 5% of pre-school children did not improve their swimming skills after taking a Beginner Swimmer Class at a certain Recreation Center. -What is the probability that a pre-school child who is taking this swim class will improve his/her swimming skills?

Use the following information for questions: A statistics class has 4 teaching assistants (TAs): three female assistants (Lauren, Rona, and Leila) and one male assistant (Josh). Each TA teaches one discussion section. -Two students, Bill and Tom, who don't know each other, each pick a discussion section. The two events B = {Bill's TA is Lauren} and T = {Tom's TA is a woman} are

Use the following information for questions: The following table provides information regarding health status and smoking status of residents of a small community (health status for individuals was measured by the number of visits to the hospital during the year). -What is the probability that a randomly selected nonsmoker made zero visits to the hospital?

If one card is randomly picked from a standard deck of 52 cards, the probability that the card will be a red suit (Heart or Diamond), or a face card (Jack, Queen, or King), or both, is